Fast Dynamic Gain Control in Cascaded Raman Fiber Amplifiers

ABSTRACT

The present invention provides methods and apparatuses for controlling a gain of a bidirectionally-pumped Raman fiber amplifier having both forward optical pumps and backward optical pumps. The overall gain is controlled by adjusting the forward optical pumps, while the power levels of the backward optical pumps are essentially fixed. Gain circuitry operates in an opened loop configuration and uses a predetermined function relating a power variation of at least one wavelength region with a pump power adjustment for at least one forward optical pump. Two approximate linear relationships between the input signal power variations and the required pump power adjustments are utilized in controlling the Raman fiber amplifier. Each approximate linear relationship includes at least one linear coefficient that relates a power variation for a specific wavelength region and a power adjustment of a specific Raman pump.

This application is a continuation-in-part of common-owned, co-pendingU.S. application Ser. No. 11/274,666 (“Fast dynamic gain control in anoptical fiber amplifier”) filed on Nov. 15, 2005 naming Xiang Zhou andMartin Birk.

FIELD OF THE INVENTION

The present invention relates to dynamically controlling the gain of anoptical fiber amplifier.

BACKGROUND OF THE INVENTION

Distributed Raman fiber amplification has been proven to be a powerfultechnique to improve the optical signal to noise ratio (OSNR) margin oflong haul wavelength-division multiplexing (WDM) system. The discreteRaman fiber amplifier is also an effective method to compensate the lossof the dispersion fiber module and/or provide extra bandwidth. A Ramanfiber amplifier can be configured either as a forward-pumped Raman fiberamplifier (RFA) or as a backward-pumped RFA. It has been shown thatusing both forward-pumped RFA and backward-pumped RFA can achieve betternoise performance and Rayleigh crosstalk performance than purelybackward pumping, and therefore enables very long span WDM transmission.On the other hand, optical communication is evolving from currentpoint-to-point systems to dynamic optical networks. In a dynamic opticalnetwork, channels will be added and dropped to meet the varying capacitydemands. In addition, accidental loss of channels due to fiber cut orfrom amplifier failure will also lead to variation of the overalloptical power in the transmission system. To keep the power of thesurviving channels at a constant level, fast dynamic gain control isindispensable for both forward-pumped distributed/discrete RFA andbackward-pumped distributed/discrete RFA, as well as EDFA's. Two controlapproaches have been demonstrated in recent years. For the firstapproach, the Raman pump powers are controlled by a closed negativefeedback loop, in which the signal gains are continuously monitored andcompared with the target gain. The error control signal is usuallygenerated through a proportional, integral and differential (PID)control algorithm. FIG. 1A shows dynamic gain control apparatus 100 fora multi-wavelength forward-pumped Raman fiber amplifier according toprior art. FIG. 1B shows dynamic gain control apparatus 150 for amulti-wavelength Backward-pumped Raman fiber amplifier according toprior art. This approach exhibits a typical control speed of tens toseveral hundred microseconds. The corresponding speed may be acceptablefor a backward-pumped distributed RFA. This approach is not typicallyfast enough for a forward-pumped RFA (either distributed or discrete),and many times even not fast enough for a backward-pumped discrete RFA,which typically has much shorter fiber length than a distributed RFA.This observation is due to the fact that the gain transients of aforward-pumped RFA are decided by the walk-off time (sub-Vs) between thesignal and the pump while a backward-pumped RFA is decided by thetransit time through the fiber (hundreds of μs for a typical distributedRFA).

The second demonstrated method is referred to the all-optical gainclamping technique, which is based on a closed optical feedback loop.However this method introduces noise degradation and is not faster thanthe first method due to the same nature (closed feedback loop). Withanother approach, a dynamic gain control scheme based on a predeterminedtable between the detected output signal power variations and therequired pump power adjustments has been proposed for a backward-pumpedRFA. Because the look-up table varies with the load (i.e., the power ofthe input signals), not only is an extra control loop needed to detectthe load, but also numerous tables are required to be stored in thecontrol circuits. This not only increases its implementationcomplexity/cost, but also slows its capability of dynamic gain control.

There is a real need in the art for a fast and efficient dynamic gaincontrol technique suitable for both forward-pumped distributed/discreteRFA and backward-pumped discrete RFA as well as other types of opticalfiber amplifiers such as Erbium doped fiber amplifiers (EDFA's).

BRIEF SUMMARY OF THE INVENTION

The present invention provides methods and apparatuses for dynamicallycontrolling a gain for cascaded Raman fiber amplifiers (RFAs). Gaincircuitry operates in an opened loop configuration and uses apredetermined function relating a power variation of at least onewavelength region with a pump power adjustment for at least one opticalpump.

With an aspect of the invention, two cascaded Raman fiber amplifiers areconfigured as a bidirectionally-pumped Raman fiber amplifier havingforward Raman pumps and backward Raman pumps coupled to an optical fiberfacility. The power levels of the backward Raman pumps are essentiallyfixed. However, the pump power adjustment is dynamically controlledusing a feed-forward dynamic gain control algorithm.

With another aspect of the invention, the feed-forward dynamic gaincontrol algorithm utilizes one of the two approximate linearrelationships.

With another aspect of the invention, each approximate linearrelationship includes at least one linear coefficient that relates apower variation for a specific wavelength region and a power adjustmentof a specific Raman pump.

With another aspect of the invention, each linear coefficient of anapproximate linear relationship is determined by experimentallyobserving or simulating an optical fiber system. Optical signal channelsare configured so that the power variations of all of the wavelengthregions may be ignored except for a specific wavelength region. Acorresponding linear coefficient is determined by dividing thecorresponding power adjustment for the specific pump by the powervariation of the specific wavelength region.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present invention and theadvantages thereof may be acquired by referring to the followingdescription in consideration of the accompanying drawings, in which likereference numbers indicate like features and wherein:

FIG. 1A shows dynamic gain control method for a multi-wavelengthforward-pumped Raman fiber amplifier according to prior art;

FIG. 1B shows dynamic gain control method for a multi-wavelengthBackward-pumped Raman fiber amplifier according to prior art;

FIG. 2 shows an experimental setup for a forward-pumped Raman fiberamplifier in accordance with an embodiment of the invention;

FIG. 3 shows Raman pump powers in a linear scale as a function of theinput signal power in a linear scale for a forward-pumped Raman fiberamplifier in accordance with an embodiment of the invention;

FIG. 4 shows Raman pump powers in a decibel scale as a function of theinput signal power in a linear scale for a forward-pumped Raman fiberamplifier in accordance with an embodiment of the invention;

FIG. 5 shows a dynamic gain control circuit for a forward-pumped Ramanfiber amplifier in accordance with an embodiment of the invention;

FIG. 6 shows a target Raman fiber amplifier gain profile in accordancewith an embodiment of the invention;

FIG. 7 shows a first example that compares gain deviation with andwithout dynamic gain control in accordance with an embodiment of theinvention;

FIG. 8 shows a second example that compares gain deviation with andwithout dynamic gain control in accordance with an embodiment of theinvention;

FIG. 9 shows a third example that compares gain deviation with andwithout dynamic gain control in accordance with an embodiment of theinvention;

FIG. 10 shows a fourth example that compares gain deviation with andwithout dynamic gain control in accordance with an embodiment of theinvention;

FIG. 11 shows a fifth example that compares gain deviation with andwithout dynamic gain control in accordance with an embodiment of theinvention;

FIG. 12 shows a sixth example that compares gain deviation with andwithout dynamic gain control in accordance with an embodiment of theinvention;

FIG. 13 shows a seventh example that compares gain deviation with andwithout dynamic gain control in accordance with an embodiment of theinvention;

FIG. 14 shows an eighth example that compares gain deviation with andwithout dynamic gain control in accordance with an embodiment of theinvention;

FIG. 15 shows a comparison of two control schemes in accordance with anembodiment of the invention;

FIG. 16 shows an experimental set up for a backward-pumped Raman fiberamplifier in accordance with an embodiment of the invention;

FIG. 17 shows Raman pump powers in a linear scale as a function of theinput signal power in a linear scale for a backward-pumped Raman fiberamplifier in accordance with an embodiment of the invention;

FIG. 18 shows Raman pump powers in a decibel scale as a function of theinput signal power in a linear scale for a backward-pumped Raman fiberamplifier in accordance with an embodiment of the invention;

FIG. 19 shows a backward-pumped Raman fiber amplifier in accordance withan embodiment of the invention;

FIG. 20 shows a backward-pumped Raman fiber amplifier in accordance withan embodiment of the invention;

FIG. 21 illustrates an example of dynamic gain control for aforward-pumped Raman fiber amplifier in accordance with an embodiment ofthe invention;

FIG. 22 illustrates an example of dynamic gain control for abackward-pumped Raman fiber amplifier in accordance with an embodimentof the invention;

FIG. 23 shows a backward-pumped Raman fiber amplifier in accordance withan embodiment of the invention;

FIG. 24 shows a backward-pumped Raman fiber amplifier in accordance withan embodiment of the invention;

FIG. 25 shows an optical fiber system that utilizes dynamic control forboth a forward-pumped Raman fiber amplifier and a backward Raman fiberamplifier in accordance with an embodiment of the invention;

FIG. 26 shows an optical fiber system that utilizes dynamic control forboth a forward-pumped Raman fiber amplifier and a backward Raman fiberamplifier in accordance with an embodiment of the invention;

FIG. 27 shows an apparatus for controlling a bidirectionally-pumpedRaman amplifier in accordance with an embodiment of the invention;

FIG. 28 shows an experimental setup for obtaining experimental resultsof a bidirectionally-pumped Raman amplifier in accordance with anembodiment of the invention;

FIG. 29 shows a graphical representation of drop pattern channel numbersin accordance with an embodiment of the invention;

FIG. 30 shows maximum gain error with a first gain profile in accordancewith an embodiment of the invention;

FIG. 31 shows maximum gain error with a second gain profile inaccordance with an embodiment of the invention;

FIG. 32 shows maximum gain error with a third gain profile in accordancewith an embodiment of the invention;

FIG. 33 shows an apparatus for controlling a bidirectionally-pumpedRaman amplifier having a plurality of wavelength regions in accordancewith an embodiment of the invention;

FIG. 34 shows an apparatus for controlling a forward-pumped Ramanamplifier and a backward-pumped Raman amplifier in accordance with anembodiment of the invention;

FIG. 35 shows an apparatus for controlling a backward-pumped Ramanamplifier to control an overall gain of two backward-pumped Ramanamplifiers in accordance with an embodiment of the invention;

FIG. 36 shows an apparatus for controlling two cascaded backward-pumpedRaman amplifiers in accordance with an embodiment of the invention; and

FIG. 37 shows an apparatus for controlling two cascaded backward-pumpedRaman amplifiers having the same pump wavelengths in accordance with anembodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

In the following description of the various embodiments, reference ismade to the accompanying drawings which form a part hereof, and in whichis shown by way of illustration various embodiments in which theinvention may be practiced. It is to be understood that otherembodiments may be utilized and structural and functional modificationsmay be made without departing from the scope of the present invention.

Definitions for the following terms are included to facilitate anunderstanding of the detailed description.

-   -   Optical fiber amplifier—a device to amplify an optical signal        from an optical fiber facility without converting the signal        from optical to electrical back again to optical energy.    -   Optical pump—a shorter wavelength laser that is used to pump a        length of optical fiber with energy to provide amplification of        one or more longer wavelengths.    -   Forward optical pump: a power source that provides power to a        signal by a co-propagating signal-pump optical interaction. An        example is a forward Raman pump that is based on Raman        interaction.    -   Backward optical pump: a power source that provides power to        signal by counter-propagating signal-pump optical interaction.        An example is a backward Raman pump that is based on Raman        interaction.

FIG. 2 shows an experimental setup 200 for a forward-pumped Raman fiberamplifier in accordance with an embodiment of the invention.Experimental setup 200 comprises signal generator 201 coupler 213,coupler 215, multiplexer 217, fiber facilities 205, Raman laser 203,optical power meter (OPM) 209, OPM 211, and optical spectrum analyzer(OSA) 207. Coupler 213 provides a portion (approximately 5%) of thegenerated power from signal generator 201 to OPM 209. Raman laserinjects power at approximately 1469 nm through wavelength-divisionmultiplexer (WDM) 217 to amplify the generated signal. The injectedpower from Raman laser 203 is measured by OPM 211 through coupler 215.The resulting signal is transmitted through fiber 205 and analyzed byOSA 207.

Experimental results from experimental setup 200 suggests that there aretwo approximate linear relationships between the input signal powervariations and the required pump power adjustments for bothforward-pumped RFA and backward-pumped RFA. (The two approximate linearrelationships will be discussed.) Consequently, in accordance with anembodiment of the invention, a dynamic gain control technique for bothforward-pumped distributed/discrete RFA and backward-pumped discrete RFAallows the pump power adjustments to be completed in only one stepwithin a very short period of time (<<1 μs) while operating in an openedloop configuration. (Prior art methods based on a closed feedback looptypically need more than 3 steps to stabilize the gain.) For aforward-pumped distributed/discrete RFA, the present method allows thepump powers to be adjusted synchronously with the input signal powervariation. (Prior art methods typically detect the output/backscatteredsignal variations and consequently require more time to stabilize theclosed loop control.)

When a Raman fiber amplifier is used in a dynamic optical network, thepump power needs to be adjusted accordingly when the input signal powervaries in order to maintain a constant gain. Experimental results fromexperimental setup 200 are indicative of a relationship between therequired pump power adjustment and the input signal power variation in aforward-pumped RFA. Experimental setup 200 includes fiber facilities205, which comprises approximately 77 km of standard single mode fiber(SSMF), which functions as the transmission fiber. Raman pump comprisesRaman fiber laser 203 (1469 nm with 3 dB spectral width≅1 nm) and thesignal is a narrow-band filtered ASE (amplified spontaneous emission)source (1580 nm with 3 dB spectral width≅1 nm). Both the input pumppower and the input signal power are monitored by optical power meters209 and 211 while the Raman gain is measured through OSA 207.

FIG. 3 shows a function 300 in which Raman pump power in a linear scaleis a function (relationship) of the input signal power in a linear scalefor a forward-pumped Raman fiber amplifier in accordance with anembodiment of the invention. The required Raman pump power 303 as afunction of the input signal power 301 (0.001 mW to 40 mW) for varioustarget various Raman gains (6 dB, 9.5 dB and 13 dB) corresponding toplots 305, 307, and 309, respectively.

FIG. 4 shows a function 400 (that is associated with function 300 asshown in FIG. 3), in which Raman pump power 403 is shown in a decibelscale as a function of the input signal power 401 as shown in a linearscale for a forward-pumped Raman fiber amplifier in accordance with anembodiment of the invention. The required Raman pump power 403 as afunction of the input signal power 401 (0.001 mW to 40 mW) for varioustarget various Raman gains (6 dB, 9.5 dB and 13 dB) corresponding toplots 405, 407, and 409, respectively.

As shown in FIGS. 3 and 4, input signal powers 301 and 401 are shown inlinear scale. One observes that the required pump power 303 is describedby an approximate linear function of the input signal power 301 if theRaman gain is not substantially large as shown in FIG. 3. If oneexpresses the required pump power in a decibel scale (as shown in FIG.4) while maintaining the input signal power in a linear scale, thelinear relationship (corresponding to plots 405, 407, and 409) appearsto hold not only for a relatively small Raman gain but also appears tohold for a relatively large Raman gain (as high as 13 dB).

In experimental setup 200 only one Raman pump and one signal areconsidered. However, embodiments of the invention utilize linearrelationships (similar to the two linear relations as shown in FIGS. 3and 4) for a forward-pumped RFA with multiple signals and multiple Ramanpumps as long as the Raman interactions between pump and pump, betweenpump and signal, and between signal and signal are not too strong (theunderlying reason is due to the same nature of the three Ramaninteractions).

In the following discussion, one assumes that there are M Raman pumpsand N signal channels. In an embodiment of the invention, the N signalsare partitioned into K wavelength regions. In an embodiment of theinvention, one selects one of two approximate linear functionsdescribing the relationship between the required individual pump poweradjustments (relative to a reference point, e.g., half-load with uniformchannel pattern) and the input signal power variations in the Kwavelength regions. The two approximate linear functions (relationships)are then given by: $\begin{matrix}{{\Delta\quad{P_{L}(j)}} \approx {\sum\limits_{k = 1}^{K}{{T_{LL}\left( {j,k} \right)}\Delta\quad{S_{L}(k)}}}} & \left( {{EQ}.\quad 1} \right) \\{{\Delta\quad{P_{d}(j)}} \approx {\sum\limits_{k = 1}^{K}{{T_{d\quad L}\left( {j,k} \right)}\Delta\quad{S_{L}(k)}}}} & \left( {{EQ}.\quad 2} \right)\end{matrix}$where ΔP_(L)(j), ΔP_(d)(j) denote the required power adjustment of thej^(th) pump in linear scale and in decibel scale, respectively, andΔS_(L)(k) denote the input signal power variation in linear scale in thek^(th) wavelength region. For a specific target Raman gain profile, thelinear coefficient T_(LL)(j,k) and T_(dL)(j,k) uniquely depend on thepassive optical link parameters such as fiber length, fiber loss andRaman gain coefficient, and therefore can be predetermined either bydirect measurement or by numerical simulation using the measured basicoptical link parameters.

Numerical results suggest that EQ. 1 and EQ. 2 both hold if the targetRaman gain is relatively small. With the increase of the target Ramangain it appears that EQ. 2 is preferable to describe the relationshipbetween the required pump power adjustments and the input signal powervariations, which agrees with experiments (as supported by experimentalsetup 200) in the case with only one pump and one signal.

FIG. 5 shows a dynamic gain control circuit 500 for a forward-pumpedRaman fiber amplifier in accordance with an embodiment of the invention.Dynamic gain control circuit 500 utilizes linear functions EQ. 1 or EQ.2 as a deterministic control algorithm for a forward-pumped Raman fiberamplifier (RFA). Dynamic gain control circuit 500 comprises coupler 503,which couples input signals 501 to fiber delay line 505. A small part ofthe input signal power is coupled out (to monitor the input signal powervariations) before it enters into the transmission fiber 507, which ispartitioned into K wavelength regions by a 1×K band wavelength-divisionmultiplexer (B-WDM) 504. (Alternatively, the embodiment may use a 1×Kpower splitter followed by K parallel bandpass filters.) The opticalpowers in the K wavelength regions (detected by K parallelphotodetectors (PDs) 509-511) are used as the input parameters tocontrol unit 513, which generates the required output pump powers515-517 of the M Raman pumps 519 deterministically through a simplelinear function calculations (either EQ. 1 or EQ. 2). Because thecontrol algorithm (EQ. 1 or EQ. 2) is direct using an opened feedbackloop configuration, the embodiment allows the pump power adjustments tobe completed in only one step within a very short period of time (<<1μs) even for a common DSP). M Raman pumps 519 inject power intotransmission fiber 507 through WDM 521.

While dynamic gain control circuit 500 shows only one amplifier stage,embodiments of the invention may support a plurality of amplifierstages, each amplifier stage being geographically located along a fiberoptic transmission facility and designed in accordance with EQ. 1 or EQ.2. Each amplifier stage may include forward-pumped RFAs, backward-pumpedRFAs, or a combination of forward-pumped RFAs and backward-pumped RFAs.

By introducing a short delay between the transmission branch and thecontrol branch with fiber delay line 505, the embodiment also allows thepowers of the pump to be adjusted synchronously with the input signalpower. The introduced delay by fiber delay line 505 is approximatelyequal to the time delay introduced by de-multiplexer 504, photodiodes509-511, control unit 513, and pumps 519. As a result, the controltechnique of the embodiment is typically faster (sub-μs) than controltechniques supported in the prior art (sub-ms).

Linear coefficient T_(dL)(j,k), which is contained in EQ. 2, may bedetermined by the following procedure for a 80-channel WDM system. Weassume that K=2 and we use half load with uniform channel patterns (1,3, . . . 79) as the reference point. First, only input signals atchannels 41, 43 to 79 are configured and the corresponding required pumppower adjustment ΔP_(d)(j) is found. T_(dL)(j,1) is then given byΔP_(d)(j)/ΔS_(L)(1) due to the observation that ΔS_(L)(2)=0. Second,only input signals at channel 1, 3 and 39 are configured andcorresponding required pump power adjustment ΔP_(d)(j) is foundT_(dL)(j,2) is then given by ΔP_(d)(j)/ΔS_(L)(2) due to the observationthat ΔS_(L)(1)=0. The same process is also applicable for the case withK>2 or K=1. From FIGS. 7-14 one observes that the embodiment, as shownin FIG. 5, has the capability to suppress the Raman gain deviation ofthe surviving channel to be below 0.2 dB for a wide range of inputsignal spectral patterns. Without using gain control, however, the Ramangain deviation of the surviving channel can be as high as 2 dB with onlyone surviving channel and as high as −1.6 dB with full 80 channels.

FIG. 6 shows a target Raman fiber amplifier gain profile 600 inaccordance with an embodiment of the invention. The chosen referenceoperation point is with half-load (40 channels) and uniform channeldistribution (1,3,5, . . . 79). As shown in FIG. 6, the Raman gainincludes both the gain from the Raman pumps and the gain from the othersignals. Choosing half load as the reference point is preferable thanthe commonly used reference point with full load because it allows therequired maximum pump power adjustment to be reduced by half.

FIG. 7 shows a first example 700 that compares gain deviation with andwithout dynamic gain control with 80 active channels in accordance withan embodiment of the invention.

As previously discussed, FIGS. 7-14 (which show the simulated signalgain deviation of the surviving channel for a 50 GHz-spaced 80-channelL-band WDM system with a four-wavelength (1458, 1469, 1483 and 1503 nm)forward-pumped RFA) demonstrate the effectiveness of the embodimentshown in FIG. 5. The linear function (EQ. 2) is used as the controlalgorithm in the control unit. As a comparison, the signal gaindeviation without gain control is also illustrated in FIGS. 7-14. 80 kmof SSMF is used as the transmission fiber and the input signal power ischosen to be −3 dBm/channel. The tapped signal is divided into twowavelength regions (i.e., K=2), 1570-1584 nm, and 1584 to 1604 nm.

FIG. 8 shows a second example 800 that compares gain deviation with andwithout dynamic gain control with 1 active channel. FIG. 9 shows a thirdexample 900 with 60 active channels. FIG. 10 shows a fourth example 1000with channels 21-80 active.

FIG. 11 shows a fifth example 1100 with 20 active channels. FIG. 12shows a sixth example 1200 with channels 31-50 active. FIG. 13 shows aseventh example 1300 with channels 61-80 active. FIG. 14 shows an eighthexample 1400 with 40 active channels. The above examples demonstrate theeffectiveness of the embodiment shown in FIG. 5.

FIG. 15 shows a plot 1500 comparing two control schemes with allchannels (1-80) active in accordance with an embodiment of theinvention. One observes that, while both schemes have the capability tosuppress the signal gain deviation effectively (peak gain deviation issuppressed from −1.6 dB to 0.15 dB by using EQ. 2, and from −1.6 dB to−0.3 dB by using EQ. 1), the algorithm based on EQ. 2 appears to bebetter than the algorithm based on EQ. 1. This observation is due to thefact the target Raman gain (10.2±0.3 dB) is not sufficiently small.Simulations were performed to investigate the impact of K on theperformance of dynamic gain control. Numerical results suggest that, fora purely L-band/C-band system, K=2 is a preferable choice, because afurther increase of K only gives minor performance improvement but mayincrease cost considerably. On the contrary, choosing K=1 is acceptabledepending on the system requirement—the peak gain deviation can besuppressed to be below 0.3 dB with K=1 while can be suppressed to bebelow 0.2 dB with K=2 for this specific WDM system. If one chooses K=1,the dynamic gain control circuit can be simplified with respect toapparatus 500 as shown in FIG. 5. The above investigations are based ona distributed RFA, although a similar approach is also applicable to adiscrete RFA, in which only the fiber length and fiber type aredifferent.

FIG. 16 shows an experimental setup 1600 for a backward-pumped Ramanfiber amplifier for investigating the relationship between the requiredpump power adjustment and the input signal power variation in accordancewith an embodiment of the invention. Experimental results suggest asimilar linear relationship (as shown in FIGS. 17 and 18) for abackward-pumped RFA as for a forward-pumped RFA (as previously discussedwith FIGS. 3 and 4.

FIG. 17 shows a function 1700 in which Raman pump power in a linearscale is a function of the input signal power in a linear scale for abackward-pumped Raman fiber amplifier in accordance with an embodimentof the invention. FIG. 18 shows a function 1800 in which Raman pumppower in a decibel scale is a function of the input signal power in alinear scale for a backward-pumped Raman fiber amplifier in accordancewith an embodiment of the invention.

As with a forward pumped RFA, an embodiment of the invention utilizesone of two approximate linear relationships between the input signalpower variations and the required pump power adjustments for thebackward-pumped RFAs that are shown in FIGS. 19 and 20. Moreover, thelinear relations are relations that are applicable to fiber systems thatutilize both a forward-pumped RFA as well as a backward-pumped RFA.

Embodiments of the invention are not limited to control schemes thatutilize linear functions corresponding to EQ. 1 or EQ. 2. Othercomplicated functions (linear or non-linear) that relate the inputsignal power variations directly to the required pump power adjustmentsare also applicable. As an example, the input signal power variationscan be separated into several power regions. Within each region, linearfunction (EQ. 1) or (EQ. 2) is used to connect the required pump poweradjustment to the input signal power variation, but the linearcoefficients are allowed to be different between different powerregions. A corresponding control algorithm may provide a better gaindeviation suppression but at the cost of control speed and complexity.

FIG. 19 shows a backward-pumped Raman fiber amplifier 1900 in accordancewith an embodiment of the invention. RFA 1900 incorporates a dynamicgain control circuit using EQ. 1 or EQ. 2 as the deterministic controlalgorithm for a backward-pumped discrete RFA is shown in FIG. 19. (RFA2000 is the simplified version for the case when K=1, where the Ramanfiber can be a conventional DCF or some special high nonlinear fiber.)Because a discrete RFA has much shorter fiber length than a distributedRFA, the gain transients experienced by a backward-pumped discrete RFAduring channel add/drop can be significantly faster than abackward-pumped distributed RFA. Due to its deterministic nature(one-step), typically the control circuits shown in FIGS. 19 and 20 areinherently faster than the conventional methods based on a closedfeedback loop, which usually needs several control cycles to stabilizethe signal gain. With an embodiment of the invention, the control speedcan be further improved by adding a proper electrical delay inside thecontrol circuit to optimize the timing of the required pump poweradjustment relative to the input signal power variation. As for thecontrol algorithm, one observes that the algorithm based on EQ. 1typically performs better than the algorithm based on EQ. 2 asillustrated by FIGS. 17 and 18. This observation is different from aforward-pumped RFA, where EQ. 2 typically performs better than EQ. 1.The underlying reason is due to the observation that pump depletion fora backward-pumped RFA occurs mostly close to the fiber end; therefore,exponential fiber loss plays a much less important role in the pumpdepletion than a forward-pumped Raman amplifier, in which the pumpdepletion occurs in a much longer fiber length.

Referring to FIG. 19, a portion the input power from input signal 1901is provided by coupler 1903 to B-WDM 1907. Photodiodes 1909-1911 measureinput power variations (PD) for each of the K wavelength regions.Control unit 1913 determines the pump power adjustments 1915-1917 usingeither EQ. 1 or EQ. 2. M pumps 1919 inject power into Raman fiber 1905in the backward direction through optical circulator (OC) 1921.

Backward-pumped Raman fiber amplifier 2000, as shown in FIG. 20, issimilar to backward-pumped Raman fiber amplifier 1900; however, withbackward-pumped Raman fiber amplifier 2000, K=1 (i.e., there is onewavelength region). Consequently, control unit 2013 processes the inputpower variation (PD) for one wavelength region through photodiode 2009.Control unit 2013 controls M pumps 1919 by providing the pump poweradjustments 2015-2017 to M pumps 1919.

FIGS. 21 and 22 provide examples that illustrate the above discussion.FIG. 21 illustrates an example of dynamic gain control for aforward-pumped Raman fiber amplifier in accordance with an embodiment ofthe invention. The following linear functions are used: $\begin{matrix}{{P_{L}\left( {j,t} \right)} \approx {{P_{L\quad 0}(j)} + {\sum\limits_{k = 1}^{K}{{T_{LL}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,t} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 3} \\{{P_{d}\left( {j,t} \right)} \approx {{P_{d\quad 0}(j)} + {\sum\limits_{k = 1}^{K}{{T_{d\quad L}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,t} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 4}\end{matrix}$where P_(L)(j,t) denotes the required pump power in the linear unit ofthe j^(th) pump at time instant t, S_(L)(k,t) denotes the detected inputsignal power in the k^(th) wavelength region also in the linear unit.S_(L0)(k) and P_(L0)(j) denotes the corresponding input signal power andpump power at the reference operation point. The subscript L and d inEQ. 3 and EQ. 4 denote linear scale and logarithmic scale, respectively.EQ. 4 appears to be preferable for a forward-pumped Raman fiberamplifier.

In the example shown in FIG. 21, K=1, corresponding to a four-wavelengthforward-pumped Raman fiber amplifier with 80 km of TW-Reach transmissionfiber functions as the gain medium. The pump wavelengths are 1425, 1436,1452 and 1466 nm. Full load (which is referred as the reference point)is configured as: 40 channel 100 GHz-spaced C-band signal, 1530 nm to1561 nm, −3 dBm/channel input signal power, and a target Raman gain of14±0.6 dB across the C-band.

The example utilizes the following linear control equation:P _(d)(j,t)≈P _(d0)(j)+T _(dL)(j)[S _(L)(t)−S ₀] where j=1,2,3,4  EQ. 5where P_(d0)(1)=24.3 dBm, P_(d0)(2)=23.0 dBm, P_(d0)(3)=21.63 dBm, andP_(d0)(4)=19.3 dBm and S_(L0)=20 mW.

Referring to FIG. 21, plot 2101 corresponds to the first pump (1425 nm),plot 2103 corresponds to the second pump (1436 nm), plot 2105corresponds to the third pump (1452 nm), and plot 2107 corresponds tothe fourth pump (1466 nm). The linear coefficients T_(dL)(1), T_(dL)(2),T_(dL)(3), and T_(dL)(4) are determined to be 0.159, 0.167, 0.115, and0.098, respectively.

FIG. 22 illustrates an example of dynamic gain control for abackward-pumped Raman fiber amplifier in accordance with an embodimentof the invention. The following dynamic control equations are used:$\begin{matrix}{{P_{L}\left( {j,t} \right)} \approx {{P_{L\quad 0}(j)} + {\sum\limits_{k = 1}^{K}{{T_{LL}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 6} \\{{P_{d}\left( {j,t} \right)} \approx {{P_{d\quad 0}(j)} + {\sum\limits_{k = 1}^{K}{{T_{d\quad L}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 7}\end{matrix}$where P_(L)(j,t) denotes the required pump power in the linear unit ofthe j^(th) pump at time instant t, S_(L)(k,t) denotes the detected inputsignal power in the k^(th) wavelength region also in the linear unit.S_(L0)(k) and P_(L0)(j) denotes the corresponding input signal power andpump power at the reference operation point. T denotes the introducedtime delay between the pump power adjustment and the input signal powervariation, roughly equal to the propagation time of the signal in thefiber. The subscript L and d in EQ. 6 and EQ. 7 denote linear scale andlogarithmic scale, respectively. EQ. 6 appears to be preferable for abackward-pumped Raman fiber amplifier.

In the example shown in FIG. 22, K=1. The example corresponds to afour-wavelength backward-pumped discrete Raman fiber amplifier with 12km of dispersion compensating fiber as the gain medium. The pumpwavelengths are 1425, 1436, 1452 and 1466 nm. Full load (referred as thereference point) is configured as: 40 channel 100 GHz-spaced C-bandsignal, 1530 to 1561 nm, −3 dBm/channel input signal power. The targetRaman gain is 16±0.6 dB across the C-band.

The example uses the following linear control equation:P _(L)(j,t)≈P _(L0)(j)+T _(LL)(j)[S _(L)(t)−S ₀] j=1,2,3,4  EQ. 7where P_(L0)(1)=246 mW, P_(L0)(2)=197.2 mW, P_(L0)(3)=122 mW, andP_(L0)(4)=140.6 mW S_(L0)=20 mW

FIG. 23 shows a backward-pumped Raman fiber amplifier in accordance withan embodiment of the invention. Apparatus 2300 supports a geographicalseparation of the detection of the input power variation (determined bycoupler 2303, B-WDM 2305, photodiodes 2307-2309, control unit 2311) andthe injection of power by M pumps 2317. In the embodiment shown in FIG.23, a portion of power from input signal 2301 is coupled by coupler 2303into B-WDM 2305 and processed by control unit 2311. Because M pumps 2317are geographically separated from control unit 2311, control informationfrom control unit 2311 to control unit 2323 is sent over a telemetrychannel using transmission fiber 2315, WDM 2313 and WDM 2321.(Transmission fiber 2315 also supports transmission of the opticalsignal channels.) The telemetry channel may be the conventional opticalsupervisory channel that is already used in most of the commercial WDMsystem. Using the control information, control unit 2323 adjusts theinjected power of M pumps 2317 into combiner 2319. One of the followingdynamic control functions is used in designing the backward-pumped Ramanamplifier shown in FIG. 23. $\begin{matrix}{{P_{L}\left( {j,t} \right)} \approx {{P_{L\quad 0}(j)} + {\sum\limits_{k = 1}^{K}{{T_{LL}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 9} \\{{P_{d}\left( {j,t} \right)} \approx {{P_{d\quad 0}(j)} + {\sum\limits_{k = 1}^{K}{{T_{d\quad L}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 10}\end{matrix}$where P_(L)(j,t) denotes the required pump power in the linear unit ofthe j^(th) pump at time instant t, S_(L)(k,t) denotes the detected inputsignal power in the k^(th) wavelength region also in linear units.S_(L0)(k) and P_(L0)(j) denotes the corresponding input signal power andthe pump power at the reference operation point. T denotes theintroduced time delay between the pump power adjustment and the inputsignal power variation, roughly equal to the propagation time of thesignal in the transmission fiber. The subscript L and d in EQ. 9 and EQ.10 denote linear scale and logarithmic scale, respectively. EQ. 9provides performance that is preferable for a backward-pumped Ramanfiber amplifier.

FIG. 24 shows a backward-pumped Raman fiber amplifier in accordance withan embodiment of the invention. Apparatus 2400 is similar to apparatus2300; however, K=1. Consequently, only one photodiode (photodiode 2407)is needed to detect input power variations (PD). Control unit 2411processes the detected input power variations in accordance with eitherEQ. 11 or EQ. 12 and sends control information to control unit 2423 overa telemetry channel on transmission fiber 2315.P _(L)(j,t)≈P _(L0)(j)+T _(LL)(j)[S _(L)(t−T)−S _(L0)]  EQ. 11P _(d)(j,t)≈P _(d0)(j)+T _(dL)(j)[S _(L)(t−T)−S _(L0)]  EQ. 12EQ. 11 provides performance that is preferable with respect to EQ. 12for a backward-pumped Raman fiber amplifier.

Embodiments of the invention support dynamic control of both aforward-pumped RFA and a backward-pumped RFA in an optical fiber systemand Erbium doped fiber or waveguide amplifiers.

FIG. 25 shows an optical fiber system that utilizes dynamic control forboth a forward-pumped Raman fiber amplifier and a backward Raman fiberamplifier in accordance with an embodiment of the invention. One of thefollowing two gain control functions is selected to control the gain ofthe forward-pumped Raman amplifier: $\begin{matrix}{{P_{L}^{F}\left( {j,t} \right)} \approx {{P_{L\quad 0}(j)} + {\sum\limits_{k = 1}^{K}{{T_{LL}^{F}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,t} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 13} \\{{P_{d}^{F}\left( {j,t} \right)} \approx {{P_{d\quad 0}(j)} + {\sum\limits_{k = 1}^{K}{{T_{d\quad L}^{F}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,t} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 14}\end{matrix}$Additionally, one of the following two gain control functions isselected to control the gain of the backward-pumped Raman amplifier:$\begin{matrix}{{P_{L}^{B}\left( {j,t} \right)} \approx {{P_{L\quad 0}^{B}(j)} + {\sum\limits_{k = 1}^{K}{{T_{LL}^{B}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 15} \\{{P_{d}^{B}\left( {j,t} \right)} \approx {{P_{d\quad 0}^{B}(j)} + {\sum\limits_{k = 1}^{K}{{T_{d\quad L}^{B}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 16}\end{matrix}$where P_(L) ^(F)(j,t) denotes the required pump power in the linear unitof the j^(th) forward pump at time instant t, S_(L)(k,t) denotes thedetected input signal power in the k^(th) wavelength region also in thelinear unit. S_(L0)(k) and P_(L0) ^(F)(j) denotes the correspondinginput signal power and forward pump power at the reference operationpoint. The subscript L and d in EQ. 13, EQ. 14, EQ. 15, and EQ. 16denote a linear scale and a logarithmic scale. The superscript F and Bdenote the forward Raman pump and the backward Raman pump. T is thepropagation time of the optical signal in the transmission fiber. EQ. 14is preferable for the forward-pumped Raman pumps, and EQ. 15 ispreferable for the backward Raman pumps. In addition, one can use anoptical supervisory channel as the telemetry channel to send the inputsignal power information to the backward Raman pump control unit.

For a WDM system using both forward-pumped distributed Raman fiberamplifier and backward-pumped distributed Raman fiber amplifier asdiscussed above, the total Raman gain comes from three differentsources: from the forward Raman pumps through signal-forward Raman pumpinteractions, from the other signals through signal-signal Ramaninteractions, and from the backward Raman pumps through signal-backwardRaman pump interactions. Because the typical effective Raman interactionlength is smaller than 40 km and a bi-directional-pumped Raman amplifieris necessary only when the span length is large (typically greater than80 km). This implies that the gain due to the co-propagating forwardRaman pumps and the gain due to the co-propagating other signal mainlycomes from the first 40 km and the Raman gain due to the backward Ramanpumps mainly comes form the final 40 km. As a result, one can treat abidirectional-pumped distributed Raman amplifier as two separateamplifiers: a forward-pumped Raman amplifier followed by abackward-pumped Raman amplifier. The control equations EQ. 13 or EQ. 14is used to control fast gain transient (sub-us) due to co-propagatingsignal-forward pump interactions and signal-signal Raman interactionswhile the control equation EQ. 15 and EQ. 16 is used to controlrelatively slow gain transient (sub-ms) due to signal-backward pumpinteractions. The control coefficients for both the forward-pumped Ramanamplifier and the backward-pumped Raman amplifier can be predeterminedeither by numerical calculation using the measured basic fiber linkparameters or by direct measurement using K predetermined input channelpatterns as follows. First, one disables all the backward Raman pumps.For each of the K input patterns, one calculates or measures therequired power adjustments of each of the M_(F) forward Raman pumpsbased on a target forward Raman gain profile (include both the gain fromthe forward Raman pumps and the gain from the signal-signal Ramaninteraction). The sets of control coefficients for the forward-pumpedRaman amplifier can then be obtained by substituting the measuredindividual forward pump power adjustments in accordance with the Kchannel patterns into EQ. 13 or EQ. 14. Second, one turns on both theforward Raman pumps and the backward Raman pumps. For each of the Kchannel patterns, one first adjusts the forward pump powers (alreadyknown from the first step), and then one measures the required poweradjustment of each of the M_(B) backward Raman pumps based on the totaltarget Raman gain profile which includes the gain from the forward Ramanpumps, from the signal-signal Raman interaction and from the backwardRaman pumps. Substituting the measured individual backward pump poweradjustments in accordance with the K channel patterns into EQ. 15 or EQ.16, one then obtains the sets of control coefficients for thebackward-pumped Raman amplifier.

FIG. 26 shows an optical fiber system that utilizes dynamic control forboth a forward-pumped Raman fiber amplifier and a backward Raman fiberamplifier in accordance with an embodiment of the invention. The opticalfiber system is similar to the optical fiber system as shown in FIG. 25;however, the number of wavelength regions is one (i.e., K=1).

Distributed Raman fiber amplification has been proven to be a powerfultechnique to improve the optical signal to noise ratio (OSNR) margin oflong haul WDM systems, and has enabled dramatic increases in thecapacity and reach of optical fiber communication systems. A Ramanamplifier can be configured as a backward-pumped Raman fiber amplifier,a forward-pumped RFA or a bi-directionally pumped RFA. It has been shownthat a bi-directionally-pumped RFA can achieve better noise and Rayleighcrosstalk performance than a purely backward-pumped/forward-pumped RFA,and therefore enable very long span transmission. Research suggests thata bi-directionally-pumped all-Raman system allows the repeater spacingto be doubled (from current 80 km per span to 160 km per span, reducingamplifier huts and therefore real estate expense by half) whileachieving comparable performance of current 80 km per span EDFA systemsfor post-1998 standard single mode fiber (SSMF). On the other hand,optical communication is evolving from current point-to-point systems todynamic optical networks. In a dynamic optical network, channels will beadded and dropped to meet the varying capacity demands. In addition,accidental loss of channels due to fiber cut or amplifier failure willalso lead to variations of the overall optical power in the transmissionsystem. To keep the power of the surviving channels at a constant level,fast dynamic gain profile control is indispensable for both EDFA andRFA.

In an embodiment of the invention, control of an overall gain formultiple cascaded RFAs is supported. The multiple cascaded RFAs may beindependent (i.e., no interaction) or dependent (with interaction). Inaccordance with the present invention, the overall gain (including thegain from both signal-pump and signal-signal Raman interactions) may becontrolled by adjusting the pump powers of only one RFA with theproposed linear/log-linear feed-forward control algorithm. The overallgain may also be controlled by adjusting the pump powers of multipleRFAs but using only one monitor (the same feed-forward signal is sharedby multiple RFAs). Experimentation suggests the effectiveness of anembodiment in a 40 channel-100 GHz spaced C-band WDM system using afour-wavelength forward-pumped RFA and a two-wavelength backward-pumpedRFA in the same transmission fiber (corresponding to two cascaded RFAswith interaction).

Experimentation suggests that simply by adjusting the pump powers of thefour forward Raman pumps using the proposed log-linear feed-forwardcontrol algorithm, the overall gain may be stabilized for 26 distinctivedrop patterns and three different gain profiles by only monitoring thetotal input signal power. Experimental results will be furtherdiscussed.

FIG. 27 shows an apparatus 2700 for controlling a bidirectionally-pumpedRaman amplifier in accordance with an embodiment of the invention. FIG.27 includes a bidirectionally-pumped RFA with M_(F) forward Raman pumps2717 and M_(B) backward Raman pumps 2721. Apparatus 2700 transmitsoptical signal channels (input signals) 2701 over transmission fiber2707. The forward Raman pump powers are fed into transmission fiber 2707through a pump-signal wavelength division multiplexer (WDM) 2719 whilethe backward Raman pump powers are fed into the transmission fiberthrough optical circulator 2723. A portion (e.g., 5%) of the total inputsignal power is coupled through coupler 2703 and detected by photodiode2709. The detected signal from photodiode 2709 is used as the input ofthe control and decision circuit 2711. Fiber delay line 2705 has similarfunctionality as fiber delay line 505 as previously discussed with FIG.5.

Control and decision circuit 2711 determines required individual pumppower adjustments P₁ 2713 through P_(M) 2715 (relative to a referenceoperational point, such as the point of full load) through a log-linearrelationship asΔP _(d)(j)≈T _(d)(j)ΔS _(L)  EQ. 17where ΔP_(d)(j) denotes the required power adjustment of the j^(th) pumpin log scale and ΔS_(L) denotes the detected total input signal powervariation in linear scale. T_(d)(j) is the control coefficient. Itdepends only on the passive optical link parameters, and therefore canbe predetermined either by direct measurement with one predeterminedchannel drop pattern or by calculation from the known fiber parameters.Fiber delay line 2705 is introduced to optimize the required pump poweradjustment relative to the input signal power variation.

EQ. 17 is a simplification of EQ. 2, where the number of wavelengthregions (K) equals one. (Embodiments may also utilize a correspondingexpression that is a simplification of EQ. 1.) However, embodiments ofthe invention support control circuit 2711 that utilizes EQ. 1 and EQ. 2in order to support more than one wavelength regions. With EQ. 1, aspreviously discussed, the required power adjustment of the j^(th) pumpis expressed in linear scale.

With an embodiment of the invention, the gain profile variation duringchannel add/drop in a bidirectionally-pumped RFA can be greatlysuppressed by only adjusting the forward Raman pump powers through afeed-forward configuration and a simple log-linear control algorithm, inwhich the required individual pump power adjustment of the forward Ramanpumps are approximated as a log-linear function of the total inputsignal power variation. With the embodiment, only one control circuit(e.g., control circuit 2711 as shown in FIG. 27) is needed, thuseliminating the need of expensive channel monitoring. (Consequently, thecost for dynamic gain profile control in a bidirectionally-pumped RFA isreduced.). Moreover, the embodiment allows the pump control speed to beaccelerated by using a simpler pump control algorithm and feed-forwardconfiguration.

FIG. 28 shows an experimental setup 2800 for obtaining experimentalresults of a bidirectionally-pumped Raman amplifier in accordance withan embodiment of the invention. The pump control algorithm is central tothe effectiveness of setup 2800. Static experimentation suggests theverification of the control algorithm (e.g., EQ. 2 or EQ. 17). Withexperimental setup 2800, flat C-band ASE source 2801 (which includes an80-channel, 50 GHz channel equalizer (or wavelength blocker)) to createup to 40 channels of sliced ASE at 100 GHz spacing. The purpose to usedepolarized ASE source 2801 as the signal source in this experiment isto eliminate uncertainty caused by polarization-related issues. About 5%of the source output is coupled to power detector PD 2809 throughcoupler 2813 to obtain the input signal for the feed-forward algorithm.The four forward Raman pumps ABCD 2805 (inner-fiber grating stabilizedFabry-Perot lasers at 1425, 1436, 1452 and 1466 nm) are combined by WDM2817 with the 40 channel source for launch into fiber 2803 at a signallevel of −3 dBm/channel. TrueWave Reach fiber is used in setup 2800because the stimulated Raman scattering (SRS) effect in such fiber ismore severe than in SSMF, thus providing a more extreme condition forverifying the control algorithm. At the end of the fiber 2803, the twobackward Raman pumps EF 2807 (external-fiber grating stabilizedFabry-Perot lasers at 1436 and 1461 nm) are fed into fiber 2803 throughoptical circulator 2819 while the signal is coupled out to OSA 2811 tomonitor spectral flatness and total Raman gain per wavelength. Threereference flat gain profiles are measured with setup 2800. For all thethree gain profiles, the launch pump powers from the two backward Ramanpumps 2807 are fixed (E=250 mW and F=358 mW as monitored through coupler2821), and the different gain profiles are achieved by purely changingthe launch pump powers from the four forward Raman pumps 2805. The twobackward Raman pumps 2807 provide about 15 dB±1.5 dB on/off Raman gainacross the 40 channel for the case with full load and forward Ramanpumps 2805 are turned off. For gain profile 1, 2 and 3, the total launchpower from four forward Raman pumps 2805 at full load case are 324.6 mW,421.6 mW, and 500.5 mW (as monitored through coupler 2815),respectively. The corresponding on/off Raman gain from forward Ramanpumps 2805 alone are 8±0.5 dB, 10+0.5 dB, and 11.5+0.6 dB, respectively.For each gain profile (profiles 1-3), 4 control coefficients (e.g., asper EQ. 17) are determined by measuring the required individual pumppower adjustments of four forward Raman pumps 2805 at one predetermineddrop pattern (with uniform 10 surviving channels).

FIG. 29 shows graphical representation 2900 of drop pattern channelnumbers in accordance with an embodiment of the invention. Survivingchannel configuration 2901 is plotted as a function of drop patternnumber 2903. After determining the control coefficients, the gainstability under 26 distinct channel drop patterns for each of the threegain profiles were tested. In an embodiment of the invention, the 26channel drop patterns are different from the pattern used for controlcoefficient determination.

In an embodiment of the invention, the required individual pump poweradjustment is obtained through a log-linear function (e.g., EQ. 17) ofthe detected total input signal power variation. The control algorithmhas been verified with 26 distinctive drop patterns and three differentgain profiles for a C-band RFA with four forward Raman pumps and twobackward Raman pumps. With the control algorithm enabled, the maximumstatic gain error (the worst channel, relative to the full load case) issuppressed to below 0.4 dB for all the 26 drop patterns and the threedifferent gain profiles, while the maximum static gain errors go up to 8dB without gain control.

FIG. 30 shows maximum gain error with a first gain profile in accordancewith an embodiment of the invention. FIG. 31 shows maximum (lain errorwith a second gain profile in accordance with an embodiment of theinvention. FIG. 32 shows maximum gain error with a third gain profile inaccordance with an embodiment of the invention. The measured maximumgain error 3001, 3101, 3201 (i.e., most severe wavelength) as a functionof drop pattern numbers 3003, 3103, and 3203 are shown with pump control(corresponding to plots 3007, 3107, and 3207) and without pump control(corresponding to plots 3005, 3105, and 3205). Without control, one cansee the gain error may be as high as 8 dB for channel pattern number 1and gain profile 3. When control enabled, however, the residual gainerror is better than 0.4 dB in all cases, suggesting that the controlalgorithm works well for widely diverse spectral loading and differentgain levels, even in a deep saturation mode.

FIG. 33 shows an apparatus 3300 for controlling a bidirectionally-pumpedRaman amplifier having a plurality of wavelength regions in accordancewith an embodiment of the invention. FIG. 33 shows an embodiment of theinvention with two cascaded RFAs, where a forward-pumped RFA has M_(F)forward Raman pumps 3317 and a backward-pumped RFA with M_(B) backwardRaman pumps 3321 using the same fiber 3307 as the gain medium and theoverall gain is controlled by only adjusting the pump power of theforward Raman pumps. A small part of the input signal power is extractedand then divided into K wavelength regions with a bandwavelength-division multiplexer (B-WDM) 3325. The total power in each ofthe K wavelength regions is then detected by a correspondingphotodetector (PD) 3309 a-3309 k to monitor the total input power ineach corresponding wavelength region, S₁ . . . S_(K), which is then sentto control unit 3311 of the forward-pumped RFA as the feed-forwardsignal. During channel add/drop, the required power adjustment (P₁ 3313. . . P_(MF) 3315, relative to a reference operating point, e.g., withfull channel load or half channel load) for each of the M_(F) forwardRaman pumps 3317 may be determined by using one of the following twolinear equations $\begin{matrix}{{P_{d}(j)} \approx {{P_{do}(j)} + {\sum\limits_{k = 1}^{K}{{T_{d\quad L}\left( {j,k} \right)}\left\lbrack {{S_{L}(k)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 18} \\{{P_{L}(j)} \approx {{P_{L\quad 0}(j)} + {\sum\limits_{k = 1}^{K}{{T_{LL}\left( {j,k} \right)}\left\lbrack {{S_{L}(k)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 19}\end{matrix}$where P_(d)(j) and P_(L)(j) denote the required powers of the j^(th)pump in log scale and linear scale, respectively, S_(L)(k) denotes thedetected input signal power in the k^(th) wavelength region as linearscaled. P_(d)(j) or P_(L0)(j) and S_(L0)(k) denote the correspondingpump and signal powers at a reference operating point. T_(dL)(j,k) andT_(LL)(j,k) denote the linear control coefficients, which depend only onthe passive optical link parameters, and therefore may be predeterminedeither by direct measurement with a K predetermined channel pattern orby calculation from the known fiber parameters. The subscript d and Ldenote log scale and linear scale, respectively. Note that EQ. 18reduces to EQ. 17 when K=1.

A fiber delay line 3326 may be introduced to compensate the possibletime delay in the control branch. A simple method for determination ofT_(dL)(j,k) and T_(LL)(j,k) is given as follows. One configures thesignal channels so that the detected signal input power is differentfrom a reference point in the k^(th) wavelength region. One thenmeasures or calculates the required power adjustment of each Raman pump(to maintain the signal power level per channel at the output of the twocascaded RFAs to the target level). Letting ΔS_(L)(k) denote thedetected static input signal power variation in the k^(th) wavelengthregion, ΔP_(d)(j) or ΔP_(L)(j) denotes the required static poweradjustment of j^(th) pump as log scaled or as linear scaled,respectively. Then one obtains T_(dL)(j,k)=ΔP_(d)(j)/ΔS_(L)(k) orT_(LL)(j,k)=ΔP_(L)(j)/ΔS_(L)(k).

The required pump power for each of the four forward-pumped Raman pumpsunder various channel patterns are calculated by using EQ. 18 or EQ. 19,in which K=1 with the determined control coefficients. (As previouslydiscussed, EQ. 18 reduces to EQ. 17 when K=1.) As an illustratedexample, EQs. 20a-20d give the four linear pump control equations forgain profile 2 in accordance with EQ. 18:P _(dBm)(1)≈21.75+0.0046(S _(mW)−20)  EQ. 20aP _(dBm)(2)≈20.49+0.011(S _(mW)−20)  EQ. 20bP _(dBm)(3)≈17.68+0.009(S _(mW)−20)  EQ. 20cP _(dBm)(4)≈20.05+0.001(S _(mW)−20)  EQ. 20dwhile EQs. 21a-21d give the corresponding equations in accordance withEQ. 19:P _(mW)(1)=149.8+1.34(S _(mW)−20)  EQ. 21aP _(mW)(2)≈112.0+1.82(S _(mW)−20)  EQ. 21bP _(mW)(3)≈58.7+0.9(S _(mW)−20)  EQ. 21cP _(mW)(4)≈101.2+0.24(S _(mW)−20) EQ. 21dwhere S_(mW) denotes the detected total input signal power (mW). Notethat the 26 channel drop patterns are different from the pattern usedfor control coefficient determination.

The above discussion is based on the static aspects. One may alsoinclude the dynamic aspects when controlling the pump powers. Letting TBdenote the response time of the backward-pumped RFA, the two dynamiccontrol equations may be given by $\begin{matrix}{{\Delta\quad{P_{d}\left( {j,t} \right)}} \approx {{\sum\limits_{k = 1}^{K}{{T_{d\quad L}^{F}\left( {j,k} \right)}\Delta\quad{S_{L}\left( {k,t} \right)}}} + {\sum\limits_{k = 1}^{K}{\left\lbrack {{T_{d\quad L}\left( {j,k} \right)} - {T_{d\quad L}^{F}\left( {j,k} \right)}} \right\rbrack\left\lbrack {\int_{0}^{TB}{\Delta\quad{S_{L}\left( {k,{t - t^{\prime}}} \right)}{f_{B}\left( t^{\prime} \right)}{\mathbb{d}t^{\prime}}}} \right\rbrack}}}} & {{EQ}.\quad 22} \\{{\Delta\quad{P_{L}\left( {j,t} \right)}} \approx {{\sum\limits_{k = 1}^{K}{{T_{LL}^{F}\left( {j,k} \right)}\Delta\quad{S_{L}\left( {k,t} \right)}}} + {\sum\limits_{k = 1}^{K}{\left\lbrack {{T_{LL}\left( {j,k} \right)} - {T_{LL}^{F}\left( {j,k} \right)}} \right\rbrack\left\lbrack {\int_{0}^{TB}{\Delta\quad{S_{L}\left( {k,{t - t^{\prime}}} \right)}{f_{B}\left( t^{\prime} \right)}{\mathbb{d}t^{\prime}}}} \right\rbrack}}}} & {{EQ}.\quad 23}\end{matrix}$where ΔP_(d)(j,t) and ΔP_(L)(j,t) denote the required power adjustmentof the j^(th) forward pump at time instant t in log scale and linearscale, respectively, and ΔS_(L)(k,t) denotes the detected input signalpower variation in linear units. T_(dL) ^(F)(j,k) and T_(LL) ^(F)(j,k)denote the linear control coefficients for the forward-pumped RFA only(the case that all the backward-pumps are turned off), while theT_(dL)(j,k) and T_(LL)(j,k) denote the linear control coefficients forthe cascaded two RFAs as is discussed in the above. f_(B)(t) is afunction related to the response function of the backward-pumped RFA. Inmany typical cases, f_(B)(t) may be approximated as $\begin{matrix}{{f_{B}(t)} = \left\{ \begin{matrix}{t/{TB}} & {t > {0\quad{and}\quad t} < {TB}} \\0 & {else}\end{matrix} \right.} & {{EQ}.\quad 24}\end{matrix}$

The first part of EQ. 22 and EQ. 23 controls the gain transient due toessentially instantaneous co-propagating signal-signal and signal-pumpRaman interaction, while the second part mainly controls the relativelyslow gain transients due to counter-propagating signal-pump Ramaninteraction.

FIG. 34 shows an apparatus 3400 for controlling a forward-pumped Ramanamplifier (corresponding to forward pumps 3417) and a backward-pumpedRaman amplifier (corresponding to backward pumps 3721) in accordancewith an embodiment of the invention. A small part of the input signalpower is extracted and then divided into K wavelength regions with aband wavelength-division multiplexer (B-WDM) 3425. The total power ineach of the K wavelength regions is then detected by a correspondingphotodetector (PD) 3409 a-3409 k to monitor the total input power ineach wavelength region, S₁ . . . S_(K), which is processed by controlunit 3411.

In the case that the events causing the input signal power variation aremanaged more slowly than the response time of a backward-pumped RFA(tens to hundreds of microseconds) or the system requirement on thetransient control speed is relaxed under some circumstances, the overallgain of the above two cascade RFAs may also be controlled by purelyadjusting the power of the backward Raman pumps 3421 using either of thefollowing two dynamic control equations $\begin{matrix}{{P_{d}\left( {j,t} \right)} \approx {{P_{do}\left( {j,t} \right)} + {\sum\limits_{k = 1}^{K}{{T_{d\quad L}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 25} \\{{P_{L}\left( {j,t} \right)} \approx {{P_{L\quad 0}\left( {j,t} \right)} + {\sum\limits_{k = 1}^{K}{{T_{LL}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}} & {{EQ}.\quad 26}\end{matrix}$where T denotes the optimal time delay between the required pump poweradjustment and the detected signal power variation. T is typicallyapproximately equal to the propagation time of the signal in the fiber3407. (As an example, events may correspond to changes of the channelreconfiguration for cascaded Raman fiber amplifiers.) Power adjustmentinformation from control circuit 3411 is sent to control circuit 3427over optical supervisory channel 3429 (which is physically provided byan optical channel that is transmitted over fiber facility 3407).Control circuit 3427 subsequently adjusts the power levels of backwardpumps 3421 in accordance with the power adjustment information. (In theembodiment, power adjustment information corresponds to results fromcalculating EQ. 25 or EQ. 26.) The power levels of forward pumps 3417are maintained at an approximately constant power level.

FIG. 35 shows apparatus 3500 for controlling a backward-pumped Ramanamplifier to control an overall gain of two backward-pumped Ramanamplifiers over two fiber facilities 3507 and 3535 in accordance with anembodiment of the invention. With apparatus 3500, the overall gain oftwo backward-pumped RFAs (which are essentially independent) iscontrolled by only adjusting the pump powers of the firstbackward-pumped RFA 3517 (associated with fiber facility 3507), whilethe pump powers of the second backward-pumped RFA 3533 (associated withfiber facility 3535) are maintained at an approximately constant powerlevel. For this case, EQ. 25 or EQ. 26 may be used as the dynamiccontrol equation, but T is roughly equal to the propagation time of thesignal in the first backward-pumped RFA.

A small part of the input signal power is extracted and then dividedinto K wavelength regions with a band wavelength-division multiplexer(B-WDM) 3525. The total power in each of the K wavelength regions isthen detected by a corresponding photodetector (PD) 3509 a-3509 k tomonitor the total input power in each wavelength region, S₁ . . . S_(K),which is then processed by control unit 3531 to adjust the firstbackward pumps 3517.

FIG. 36 shows an apparatus 3600 for controlling two cascadedbackward-pumped Raman amplifiers in accordance with an embodiment of theinvention. With the embodiment, the overall gain of two backward-pumpedRFAs (corresponding to pumps 3517 and 3533) is controlled by adjustingthe pump powers of both RFAs but using the same feed-forward signal. EQ.25 or EQ. 26 may be used as the dynamic control equation for both RFAsbut with different control coefficients. The time delay T for the firstbackward-pumped RFA 3517 is approximately equal to the propagation timeof the signal in the first backward-pumped RFA while the time delay Tfor the second backward-pumped RFA 3633 is approximately equal to thepropagation time of the signal in both backward-pumped RFAs

A small part of the input signal power is extracted and then dividedinto K wavelength regions with a band wavelength-division multiplexer(B-WDM) 3625. The total power in each of the K wavelength regions isthen detected by a corresponding photodetector (PD) 3609 a-3609 k tomonitor the total input power in each wavelength region, S₁ . . . S_(K),which is then processed by control unit 3631 to adjust the backwardpumps 3617 and 3633.

FIG. 37 shows apparatus 3700 for controlling two cascadedbackward-pumped Raman amplifiers having the same pump wavelengths inaccordance with an embodiment of the invention. Apparatus 3700 issimilar to apparatus 3600, as previously discussed. However, pumps 3735support Raman amplification for both fiber facility 3707 and fiberfacility 3735 through coupler 3737 and through optical circulators 3739and 3741, respectively. Control circuit 3731 determines the poweradjustment for each pump using EQ. 25 or EQ. 26. (The pump powerslaunched into fiber facilities 3707 and 3735 may be different by usingdifferent power splitting ratio of coupler 3707.)

The configurations shown in FIGS. 35-37 support cascaded backward-pumpedRaman amplifiers. Moreover, embodiments of the invention supportconfigurations having cascaded forward-pumped Raman amplifiers in lieuof cascaded reverse-pumped Raman amplifiers. Accordingly, M1 forwardRaman pumps are coupled to a first fiber facility through a firstwavelength-division multiplexer (WDM), and M2 forward Raman pumps arecoupled to a second fiber facility through a second wavelength-divisionmultiplexer.

As with the configurations having cascaded backward-pumped Ramanamplifiers, EQ. 25 or EQ. 26 may be applied. For the case with cascadedforward-pumped Raman amplifiers, T is approximately equal to zero, but afiber delay line may be added into the signal path to synchronize thetransmitted signal and the control signal.

Referring to FIGS. 35-37, embodiments of the invention also supportcascaded RFA configurations, in which a forward-pumped Raman amplifieris associated with one of the fiber facilities and a backward-pumpedRaman amplifier is associated with the other fiber facility. Moreover,only one Raman fiber amplifier is adjusted to adapt to dynamic channelloading, while the pump power levels of the other Raman fiber amplifierare maintained at approximately constant values. When determiningadjusted values of the adjustable Raman amplifier, one may utilize EQ.25 or EQ. 26 as previously discussed. The time delay T between therequired pump power adjustment and the detected input signal powervariation depends on the location of the amplifier requiring pump poweradjustment, which is approximately equal to the propagation time ofsignal from the signal power monitoring point to the entering point ofthe adjusted pump power. In addition, a cascaded Raman amplifierconfiguration may include more than two Raman fiber amplifiers, e.g.,three or four Raman fiber amplifiers. Each of Raman fiber amplifiers maybe a forward-pumped Raman fiber amplifier or a backward-pumped Ramanfiber amplifier. (For example, the constituent Raman fiber amplifiersmay be a combination of forward-pumped Raman amplifiers andbackward-pumped Raman amplifiers.) Gain transients generated from thecascaded Raman fiber amplifiers are controlled by adjusting the Ramanpumps of only one Raman amplifier through a linear/log linearfeed-forward gain control circuit or by adjusting the Raman pumps of allthe Raman fiber amplifiers using the same feed-forward signal (i.e.,signal power variation is monitored only at one point).

Embodiments of the invention may support a number of cascaded RFAs thatis greater than two. Active or passive components/subsystems may beadded between two cascaded RFAs. In addition, the proposed feed-forwardcontrol circuit may be the only gain transient control circuit; however,a combination of the proposed feed forward control technique and thetraditional feed-back control technique may also be used for overallgain control. For example, the fast feed-forward gain control techniquemay be used to control very fast gain transients due to co-propagatingsignal-signal Raman interaction and signal-pump Raman interaction (if aforward-pumped RFA is used), while the traditional feedback-basedcontrol technique is used to control relatively slow counter-propagatingsignal-pump Raman interaction in a backward-pumped RFA.

Embodiments of the invention also support gain control for aconventional EDFA/EDWA amplifier, which can be viewed as a variant ofthe discrete Raman amplifier.

Finally, one observes that, if the transmission fiber is replaced by anErbium doped fiber/waveguide, and the pump wavelength are chosen to be980 nm and/or 1480 nm, the above considerations are also applicable tothe dynamic gain control for an Erbium-doped fiber/waveguide amplifier.Embodiments may support a bi-directionally-pumped Raman fiber amplifieror a bi-directionally-pumped Erbium doped fiber amplifier.

As can be appreciated by one skilled in the art, a computer system withan associated computer-readable medium containing instructions forcontrolling the computer system can be utilized to implement theexemplary embodiments that are disclosed herein. The computer system mayinclude at least one computer such as a microprocessor, digital signalprocessor, and associated peripheral electronic circuitry. Otherhardware approaches such as DSP (digital signal processor) and FPGA(field programmable gate array) may also be used to implement theexemplary embodiments.

While the invention has been described with respect to specific examplesincluding presently preferred modes of carrying out the invention, thoseskilled in the art will appreciate that there are numerous variationsand permutations of the above described systems and techniques that fallwithin the spirit and scope of the invention as set forth in theappended claims.

1. A method for controlling a total gain of cascaded Raman fiber amplifiers in an optical fiber system that supports a plurality of optical signal channels, the method comprising: (a) determining an input signal power variation for at least one wavelength region, the plurality of optical signal channels being associated with the at least one wavelength region, wherein K denotes a number of wavelength regions; (b) determining a pump power adjustment for an adjustable optical pump using a dynamic control equation, the dynamic control equation relating the input signal power variation for the at least one wavelength region to the pump power adjustment for the adjustable optical pump, the dynamic control equation depending on a response time of the cascaded Raman fiber amplifiers and on a time instant; and (c) adjusting the adjustable optical pump in accordance with the pump power adjustment.
 2. The method of claim 1, wherein: (1) the cascaded Raman fiber amplifiers include a forward-pumped Raman fiber amplifier having at least one forward optical pump and a backward-pumped Raman fiber amplifier having at least one backward optical pump, (2) the adjustable optical pump being the at least one forward optical pump, and (3) the dynamic control equation including a first component and a second component, the first component corresponding to a first gain transient resulting from an essentially instantaneous co-propagating signal-to-signal and signal-to-pump Raman interaction, the second component corresponding to a second gain transient resulting from a counter-propagating signal-to-pump Raman interaction.
 3. The method of claim 1, wherein: (1) the cascaded Raman fiber amplifiers include a forward-pumped Raman fiber amplifier having at least one forward optical pump and a backward-pumped Raman fiber amplifier having at least one backward optical pump, (2) the adjustable optical pump being the at least one backward optical pump, and (3) the response time being a time delay between the pump power adjustment and the input signal power variation.
 4. The method of claim 2, the forward pump power adjustment for the j^(th) forward optical pump with a logarithmic scale, the first component comprising: ${\sum\limits_{k = 1}^{K}{{C_{dL}^{F}\left( {j,k} \right)}\Delta\quad{S_{L}\left( {k,t} \right)}}},\quad{wherein}$ t denotes the time instant, C_(dL) ^(F)(j,k) denotes a linear control coefficient for the forward-pumped Raman fiber amplifier and ΔS_(L)(k,t) denotes the input signal power variation.
 5. The method of claim 4, the second component comprising: ${\sum\limits_{k = 1}^{K}{\left\lbrack {{C_{dL}\left( {j,k} \right)} - {C_{dL}^{F}\left( {j,k} \right)}} \right\rbrack\left\lbrack {\int_{0}^{TB}{\Delta\quad{S_{L}\left( {k,{t - t^{\prime}}} \right)}{f_{B}\left( t^{\prime} \right)}{\mathbb{d}t^{\prime}}}} \right\rbrack}},\quad{wherein}$ TB denotes a response time of the backward-pumped Raman fiber amplifier, C_(dL)(j,k) denotes a linear control coefficient for the cascaded Raman fiber amplifiers, and f_(B)(t) is a response function of the backward-pumped Raman fiber amplifier.
 6. The method of claim 5, the response function being approximated by: ${f_{B}(t)} = \left\{ \begin{matrix} {t/{TB}} & {t > {0\quad{and}\quad t} < {TB}} \\ 0 & {else} \end{matrix} \right.$
 7. The method of claim 2, the forward pump power adjustment for the j^(th) forward optical pump with a linear scale, the first component comprising: ${\sum\limits_{k = 1}^{K}{{C_{LL}^{F}\left( {j,k} \right)}\Delta\quad{S_{L}\left( {k,t} \right)}}},\quad{wherein}$ t denotes the time instant, C_(LL) ^(F)(j,k) denotes a linear control coefficient for the forward-pumped Raman fiber amplifier, and ΔS_(L)(k,t) denotes the input signal power variation.
 8. The method of claim 7, the second component comprising: ${\sum\limits_{k = 1}^{K}{\left\lbrack {{C_{LL}\left( {j,k} \right)} - {C_{LL}^{F}\left( {j,k} \right)}} \right\rbrack\left\lbrack {\int_{0}^{TB}{\Delta\quad{S_{L}\left( {k,{t - t^{\prime}}} \right)}{f_{B}\left( t^{\prime} \right)}{\mathbb{d}t^{\prime}}}} \right\rbrack}},\quad{wherein}$ TB denotes a response time of the backward-pumped Raman fiber amplifier, C_(LL)(j,k) denotes a linear control coefficient for the cascaded Raman fiber amplifiers, and f_(B)(t) is a response function of the backward-pumped Raman fiber amplifier.
 9. The method of claim 8, the response function being approximated by: ${f_{B}(t)} = \left\{ \begin{matrix} {t/{TB}} & {t > {0\quad{and}\quad t} < {TB}} \\ 0 & {else} \end{matrix} \right.$
 10. The method of claim 3, the dynamic control equation including a component comprising: ${{P_{d}\left( {j,t} \right)} \approx {{P_{do}\left( {j,t} \right)} + {\sum\limits_{k = 1}^{K}{{T_{dL}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}},$ wherein k corresponds to a k^(th) wavelength region, t corresponds to the time instant, j corresponds to a j^(th) forward Raman pump, P_(d)(j,t) denotes a required power of the j^(th) pump in a logarithmic scale, P_(d0)(j,t) and S_(L0)(k) denote a pump power and a signal power at a reference operating point, T_(dL)(j,k) corresponds to a linear coefficient relating the forward pump power adjustment of the j^(th) forward Raman pump and the input signal power variation for the k^(th) wavelength region, S_(L)(k,t−T) denotes a detected input signal power in the k^(th) wavelength region as linearly scaled, and T denotes the time delay.
 11. The method of claim 3, the dynamic control equation including a component comprising: ${{P_{L}\left( {j,t} \right)} \approx {{P_{L\quad 0}\left( {j,t} \right)} + {\sum\limits_{k = 1}^{K}{{T_{LL}\left( {j,k} \right)}\left\lbrack {{S_{L}\left( {k,{t - T}} \right)} - {S_{L\quad 0}(k)}} \right\rbrack}}}},$ wherein k corresponds to a k^(th) wavelength region, t corresponds to the time instant, j corresponds to a j^(th) forward Raman pump, P_(L)(j,t) denotes a required power of the j^(th) pump in a linear scale, P_(L0)(j,t) and S_(L0)(k) denote a pump signal and a signal power at a reference operating point, T_(LL)(j,k) corresponds to a linear coefficient relating the forward pump power adjustment of the j^(th) forward Raman pump and the input signal power variation for the k^(th) wavelength region, S_(L)(k,t−T) denotes a detected input signal power in the k^(th) wavelength region as linearly scaled, and T denotes the time delay.
 12. A method for controlling a total gain of cascaded Raman fiber amplifiers that include a forward-pumped Raman fiber amplifier having at least one forward optical pump and a backward-pumped Raman fiber amplifier having at least one backward optical pump in an optical fiber system that supports a plurality of optical signal channels, the cascaded Raman fiber amplifiers having a feed-forward configuration, the method comprising: (a) determining an input signal power variation for at least one wavelength region, the plurality of optical signal channels being associated with the at least one wavelength region, wherein K denotes a number of wavelength regions; (b) determining a forward pump power adjustment for the at least one forward optical pump using a dynamic control equation, the dynamic control equation including a first component and a second component, the first component corresponding to a first gain transient resulting from an essentially instantaneous co-propagating signal-to-signal and signal-to-pump Raman interaction, the second component corresponding to a second gain transient resulting from a counter-propagating signal-to-pump Raman interaction, the dynamic control equation relating the input signal power variation for the at least one wavelength region to the forward pump power adjustment for the at least one forward optical pump; and (c) adjusting the at least one forward pump optical pump in accordance with the forward pump power adjustment. 